There are several Roller Coaster rating/ranking sites online that, while taking some objective measures into account, heavily rely on subjective input to determine the rating or ranking of a particular roller coaster (e.g., an "excitement"or "experience" score of an "expert" rider to measure "thrill").

This Illustrative Mathematics task provides students with an opportunity to engage in Standard for Mathematical Practice 6, attending to precision. It intentionally omits some relevant information. The incompleteness of the problem statement makes the task more amenable to having students do work in groups.

The purpose of this task is to provide an opportunity for students to look for structure when comparing equations and to reason about their equivalence.

Students are asked to write an equation for a function (linear, quadratic, or exponential) that models the relationship between the elevation of the tram and the number of minutes into the ride.

The context here is a familiar one: a cold beverage warms once it is taken out of the refrigerator. Rather than giving the explicit function governing this warmth, a graph is presented along with the general form of the function. Students must then interpret the graph in order to understand more specific details regarding the function.

Consider a school where most of the students are from rural areas so they must be bused. The buses might pick up all the students and go to the elementary school and then continue from that school to pick up more students for the high school.

A clear alternative would be to have separate buses for each school even though they would need to trace over the same routes. There are, of course, restrictions on time (no student should be in the bus more than an hour), drivers, equipment, money and so forth.

How can you set up school bus routes to optimize budget dollars while balancing the time on the bus for various school groups? Build a mathematical model that could be used by various rural and perhaps urban school districts. How would you test the model prior to implementation? Prepare a short article to the school board explaining your model, its assumptions, and its results.

Finding lost objects is not always an easy task, even when you have knowledge of a general location. Consider the following scenario: you have lost a small object, such as a class ring, in a small park see map 1. It is getting dark and you have your pen light flashlight available. If your light shines on the ring, you assume that you see it. You cannot possibly search 100% of the region. Determine how you will search the park in minimum time. An average person walks approximately 4 mph. You have about 2 hours to search. Determine the chance you will find the lost object.https://mathmodels.org/Problems/2011/HIMCM-B/index.html

This Illustrative Mathematics task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the business.

This task is intended primarily for instructional purposes. It provides a concrete geometric setting in which to study rigid transformations of the plane

As online stores start to compete with traditional brick and mortar stores the goal is to combine the benefits of both types of businesses. Brick and mortar stores provide the benefit of seeing the actual items, picking up your purchase right away, and not having to pay for shipping. But, sometimes the store is not convenient to your location, or you do not have time to go shopping. Online stores offer the convenience of shopping from home and the added benefit, in many cases, of no additional sales or other taxes. And, with international shipping, many more items are available to shoppers all over the globe via the Internet. For the purposes of this HiMCM problem, we will use an example from the United States.

This task provides experience working with transformations of the plane and also an abstract component analyzing the effects of the different transformations.

The purpose of this task is to work with transformations to exhibit triangle congruences in a general setting.

Winter is coming! In February 2018, PyeongChang, South Korea will host the Winter Olympics. And, in 2022, Beijing, China will be the host city. The Winter Olympics have over fifty ski related events in the disciplines of Alpine, Nordic, Cross-Country, Ski Jumping, Snowboarding, and Freestyle.

Skyscrapers vary in height , size (square footage), occupancy rates, and usage. They adorn the skyline of our major cities. But as we have seen several times in history, the height of the building might preclude escape during a catastrophe either human or natural (earthquake, tornado, hurricane, etc). Let's consider the following scenario. A building (a skyscraper) needs to be evacuated. Power has been lost so the elevator banks are inoperative except for use by firefighters and rescue personnel with special keys.

Build a mathematical model to clear the building within X minutes. Use this mathematical model to state the height of the building, maximum occupation, and type of evacuation methods used. Solve your model for X = 15 minutes, 30 minutes, and 60 minutes.

Fire is one of the leading causes of accidental deaths. It is important for everyone to take every preventative measure and precaution possible to be ready to deal with a fire emergency.
More than half of all fatal fires occur between 10 p.m. and 6 a.m. when everyone in the home is usually asleep. Smoke alarms are necessary to alert you to fires when you sleep. Will smoke alarms allow enough time to evacuate safely?

This task has students approach a function via both a recursive and an algebraic definition, in the context of a famous game of antiquity that they may have encountered in a more modern form.

The task is a seemingly straightforward modeling task that can lead to more involved tasks if the instructor expands on it. In this task, students also have to interpret the units of the input and output variables of the solar radiation function.

The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations.